In the system as shown, mass of the block is 1kg and spring constant is 25 N/m. The maximum kinetic energy of the block is 50J :

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At half of the amplitude, the kinetic energy is 37.5J

The amplitude of oscillation is 2m

At half of the amplitude potential energy of the spring is 12.5J

At half of the amplitude, potential energy of the spring is 20J

answer is A, B, C.

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Detailed Solution

$ω = \sqrt{K / m} = 5 r a d / \sec$
$\frac{1}{2} m v^{2} \max = (\frac{1}{2}) (1) (ω^{2} A^{2}) = \frac{1}{2} (25 A^{2}) = 50 J \Rightarrow$ A=2m
$U_{A / 2} = \frac{1}{2} K x^{2} = (\frac{1}{2}) (25) (1) = 12.5 J$
$V_{A / 2} = ω {(A^{2} - x^{2})}^{1 / 2} = 5 \sqrt{3}$
$K_{A / 2} = \frac{1}{2} m v^{2} = (\frac{1}{2}) (1) {(5 \sqrt{3})}^{2} = 37.5 J$